# $* d *$ operator — Digest the (differential/geometry) meaning

I like to digest better:

• the $$* d *$$ operator in Maxwell differential form equation

• the $$* D *$$ operator in Yang-Mills differential form equation

We already knew that in Maxwell differential form equation we have: $$* d * F=0$$ knew that in Yang-Mills differential form equation we have: $$* D * F=0$$ here $$D .=d .+ [A,.]$$

But how we do understand $$* d *$$ operator and $$* D *$$ operator? Their the (differential/geometry) meaning? How do we make ourselves comfortable , even though we also knew the equation boils down to:

$$\partial_\mu F^{\mu \nu}=0$$ $$D_\mu F^{\mu \nu}=0$$ respectively. But how to think $$* d *$$ operator and $$* D *$$ operator differential/geometry-ly?

• Well, do you understand what $\ast$ and $d$ individually mean? – d_b May 20 at 21:46